Gain of regularity for the relativistic collision operator

TL;DR

This paper investigates the regularity properties of the gain part of the relativistic Boltzmann collision operator, covering a wide range of potentials with angular cut-off, advancing understanding of relativistic kinetic theory.

Contribution

It establishes regularity results for the gain collision operator in the relativistic Boltzmann equation under broad assumptions on the scattering kernel.

Findings

Proves regularity for the gain part of the relativistic collision operator.

Applies to full range of hard and soft potentials with angular cut-off.

Enhances mathematical understanding of relativistic kinetic equations.

Abstract

We study a regularity property for the gain part of the relativistic Boltzmann collision operator. Our assumptions on the collisional scattering kernel cover the full range of generic hard and soft potentials with angular cut-off.